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Design of vector autoregressive processes for invariant statistics

  • Paruolo Paolo


    (Department of Economics, University of Insubria, Italy)

This paper discusses the Monte Carlo (MC) design of Gaussian Vector Au- toregressive processes (VAR) for the evalutation of invariant statistics. We focus on the case of cointegrated (CI) I(1) processes, linear and invertible trans- formations and CI rank likelihood ratio (LR) tests. It is found that all VAR of order 1 can be reduced to a system of independent or recursive subsystems, of computational dimension at most equal to 2. The results are applied to the indexing of the distribution of LR test statistics for CI rank under local alternatives. They are also extended to the case of VAR processes of higher order.

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Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0504.

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Length: 31 pages
Date of creation: Sep 2005
Date of revision:
Handle: RePEc:ins:quaeco:qf0504
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  1. Saikkonen, Pentti & Lütkepohl, Helmut, 1998. "Testing for the cointegrating rank of a VAR process with an intercept," SFB 373 Discussion Papers 1998,51, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Toda, Hiro Y, 1994. "Finite Sample Properties of Likelihood Ratio Tests for Cointegrating Ranks when Linear Trends are Present," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 66-79, February.
  3. Peter Reinhard Hansen, 2005. "Granger's representation theorem: A closed-form expression for I(1) processes," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 23-38, 03.
  4. Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
  5. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  6. Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2001. "Maximum eigenvalue versus trace tests for the cointegrating rank of a VAR process," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 8.
  7. Bent Nielsen, 2004. "On the Distribution of Likelihood Ratio Test Statistics for Cointegration Rank," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 1-23.
  8. Gonzalo, Jesus, 1994. "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233.
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